Triggering Dissymmetry in Achiral Dye Molecules by Chiral Solvents:
Circular Dichroism Experiments and DFT Calculations
SERGIO ABBATE,1,2* FRANCE LEBON,1,2GIOVANNA LONGHI,1,2MARCO PASSARELLO,1,3
ANDVINCENZO TURCO LIVERI3 1
Dipartimento di Scienze Biomediche e Biotecnologie, Universita` di Brescia, Viale Europa 11, 25123 Brescia, Italy 2CNISM, Consorzio Interuniversitario Scienze Fisiche della Materia, Via della Vasca Navale 84, 00146 Roma, Italy 3
Dipartimento di Chimica ‘‘S. Cannizzaro,’’ Universita` degli Studi di Palermo, Viale delle Scienze Parco d’Orleans II, 90128 Palermo, Italy
ABSTRACT The electronic circular dichroism spectra of achiral product ‘‘Lumogen F Red’’ (ROT-300) in four different chiral solvents are recorded at different temperatures. DFT calcula-tions allow to identify two enantiomeric conformers for ROT-300. In vacuo they are equally populated; in chiral solvents one enantiomer prevails. Thermodynamic quantities involved in the chiral preference are derived. Chirality 23:910–915, 2011. VVC 2011 Wiley-Liss, Inc.
KEY WORDS: circular dichroism (CD); time-dependent density functional theory (TDDFT); dye molecules, solvent effect
INTRODUCTION
The solvent dependence of chiroptical spectra has been the theme of several studies; data have been reported for op-tical rotation or opop-tical rotatory dispersion,1–3for electronic circular dichroism (ECD)4–7 and for vibrational circular
dichroism (VCD).8,9 In the cited ECD and VCD cases two effects were monitored: the change of intensity of ECD and VCD signals and/or the shift of the center-band frequencies of ECD or VCD bands of chiral molecules by different sol-vents, due to solvent polarity; sometimes the induction of some asymmetry by the solute chiral molecules onto achiral solvents was observed and explained.9,10Here we report on a case, where an achiral compound, whose commercial name is Lumogen Red 300, i.e., N,N0 -bis(2,6-diisopropylphenyl)-1,6,7,12-tetraphenoxyperylene-3,4:9,10-tetracarboxydiimide (see Scheme 1) is dissolved in several chiral solvents. ROT-300 is a dye molecule that is under investigation for possible use as a laser-active substance.11It consists of a central pery-lenep-conjugated system with four O-phenyl pendant groups and two terminal conjugated systems bonded through N-atoms to the central moiety. A previous investigation12exists
based on HPLC, NMR, and CD on similar molecules, whose enantiomers had been separated and studied in achiral sol-vents.
EXPERIMENTAL AND CALCULATIONS
ROT-300 has been obtained from Kremer Pigmente which sells the product synthetized in the BASF laboratory in Germany.
ROT-300 was dissolved in several chiral solvents, namely (2)-diethyl
D-tartrate and (1)-diethylL-tartrate; (R)-(1)-methyl lactate and
(S)-(2)-methyl lactate; (R)-(2)-carvone and (S)-(1)-carvone, and (R)-(1)-phenyl-ethanol and (S)-(2)-phenylethanol at 2.2 3 1024M concentration.
ECD and UV absorption spectra were taken simultaneously on a Jasco 815-SE spectropolarimeter in a thermostated 1 mm quartz cylindrical cell (for the phenylethanol solutions in the 280–400 nm range we used a 2.2 3 1023M solution in 0.1 mm cell), averaging over 10 scans (s 5 2 s, scanning speed5 100 nm/min, spectral bandwidth 5 1 nm) and spectra were solvent substracted. Other concentrations were tested by ECD at room temperature for the diethyl tartrate solvents, ranging from 2.23 1025M to 1023M (and for UV spectra from 2.23 1026M).
The geometry optimization of a single ROT-300 molecule in vacuo was calculated with Gaussian 0913 using the B3LYP functional and the
6-31G* basis set. ECD spectra were calculated using time-dependent DFT calculations (TD-DFT)14at the same functional and basis set level con-sidering 14 excited states.
e and De have been evaluated from the calculated dipole and rotational strengths and a width of 0.14 eV applied to Lorentzian bands gives a good fitting with the experimental data.
RESULTS AND DISCUSSION
Solutions of ROT-300 in four enantiomeric couples of the chiral solvents (2)-diethyl D-tartrate and (1)-diethyl L
-tar-trate; (1)-methyl lactate and (S)-(2)-methyl lactate; (R)-(2)-carvone and (S)-(1)-carvone, and (R)-(1)-phenylethanol and (S)-(2)-phenylethanol) were prepared. Some other com-mercial chiral solvents were tried but we did not get positive results, mainly due to low solubility. ECD and UV absorption spectra were taken simultaneously to properly evaluate the dissymmetry g factor and were presented in Figure 1 (panels a–d).
In Figure 1 one may observe that enantiomeric solvents produce enantiomeric ECD spectra in the region where just ROT-300 absorbs. All spectra look similar in shape, though with different DA, meaning to us that the ROT molecule is subject to the same phenomena in different chiral solvents, but to different extent. The observed mirror-image appear-ance of ECD spectra in enantiomeric solvents guarantees that the data are reliable; theDA values observed are for con-centrations ranging from 1024 to 1023M, but concentration times pathlength is equal in all cases and thus theDA values are directly comparable.
For completeness, in panel e of Figure 1 we report the UV spectra of ROT-300 in the four solvents (of course in this case the UV data relative to only one enantiomeric species is needed).
Additional Supporting Information may be found in the online version of this article.
Contract grant sponsor: Italian ‘‘Ministero dell’Istruzione, dell’Universita` e della Ricerca’’ (MIUR); Contract grant numbers: PRIN 2008LYSEBR. *Correspondence to: Sergio Abbate, Dipartimento di Scienze Biomediche e Biotecnologie, Universita` di Brescia, Viale Europa 11, 25123 Brescia, Italy. E-mail: abbate@med.unibs.it
Received for publication 18 April 2011; Accepted 21 June 2011 DOI: 10.1002/chir.21012
Published online 26 September 2011 in Wiley Online Library (wileyonlinelibrary.com).
V
All ECD spectra are similar and present a broad struc-tured asymmetric feature at about 580 nm. In the different solvents the region between 480 nm and 350 nm shows bands of opposite sign and smaller intensity. Finally at about 300 nm one observes, except for the carvone solution, which is not transparent in that range, a narrow and fairly intense ECD band with the same sign as the 580 nm broad ECD band.
The observed ECD bands correspond to the observed UV absorption bands. Due to better signal to noise ratio of UV data with respect to ECD data, one may safely assume that in phenylethanol there is a definite red-shift of the UV band to 585 nm with respect to the other solvents. The same effect may be observed on the ECD band at about 580 nm, even though the data are noisier, being less intense.
In Supporting Information (Figs. S1–S3), we report CD, absorption and fluorescence spectra of ROT-300 in diethyl-D
-tartrate and diethyl-L-tartrate at different concentration values
to show that the observed CD signals can be assumed as due to the isolated ROT-300 molecule; aggregation has minimal influence.
A clue for understanding why enantiomeric ECD spectra of ROT-300 compounds are generated when enantiomeric solvents are used is found by performing DFT calculations. The optimized structure obtained with the programs’
pack-Scheme 1. Molecular formula of ROT-300 with atom numbering estab-lished by the Chemistry software tool employed by us.
Fig. 1. ECD spectra of ROT-300 in: (a) (1)-diethylL-tartrate (gray) and (2)-diethylD-tartrate (black) (DLT and DDT, respectively); (b) (R)-(1)-methyl-lactate (gray) and (S)-(2)-methyl-lactate (black); (c) (R)-(2)-carvone (gray) and (S)-(1)-carvone (black); (d) (R)-(1)-phenylethanol (gray); and (S)-(2)-phenylethanol (black); (e) UV of ROT-300 in DLT (a), S(2)ML (b), (R)-(2)-carvone (c) and (S)-(2)-phenylethanol (d). For phenylethanol, the UV and ECD spectra between 280 and 400 nm were obtained with the 0.1mm cell; 2.23 1023M.
age Gaussian0913 is presented in Figure 2. An overall dis-symmetric structure is indeed observed even by mere inspection of Figure 2; it consists in the distorted central per-ylene unit, reminding the form of a twisted ribbon, in the asymmetric arrangement of the four O-phenyl groups in the periphery of the central perylene moiety, in the dihedral angle formed by the two planes containing the terminal N-phenyl-isopropyl groups being different from zero and finally in the four isopropyl groups attached to the two terminal N-phenyl groups being twisted. The structure of Figure 2 may be defined of P-type, according to the accepted nomencla-ture.15 Of course the opposite M-type structure, has equal energy as the P one, while the flat achiral structure has higher energy and is not a minimum. In Table 1 we report the values for the relevant dihedral angles of ROT-300, allow-ing us to quantitatively measure the distortion from planarity. From Table 1 we conclude that an overall distortion of the molecular backbone of about 308 is predicted on the basis of DFT calculations, as measured by the dihedral angle 15-21-36-32 (ca, 328). This distorted dihedral angle has a value equal to those observed for the two sides of the perylene, on the left (16-17-28-31) and on the right (20-19-30-37) in Figure 2. The distorsion involves also the relative angle between the two terminal N-phenyl-isopropyl groups (1-5-45-43) and the relative dihedrals of the isopropyls at one terminal with respect to the isopropyls at the other one (22-4-46-47 and 25-2-42-50). On top of that overall distortion, lateral O-phenyl groups show further distortions. From a first conformational analysis, these lateral groups present angles (like 19-20-53-57) with values about 61608 and phenyls are oriented grossly perpendicular to the COC plane (60–908), without much change in energy among the different allowed orienta-tions about the CO. The previous study of Ref. 12 arrived at similar conclusions on other perylene-based molecules, by AM1 calculations.
The TDDFT calculated ECD spectra are not identical for different O-phenyl orientation, but the first transition at about
570 nm, HOMO-LUMO, involves just the central perylene part of the molecule. UV and ECD spectra derived for the chiral P-conformer of ROT-300 shown in Figure 2, are reported in Figure 3 where bars are proportional to calcu-lated dipole and rotational strengths. The calcucalcu-lated spectra are superimposed to the corresponding experimental spec-tra. One may see that a good prediction is obtained in fre-quencies and intensities for the UV spectra, while in the CD case there is a good correspondence between calculated and experimental frequencies and signs only.
The observed rotational strengths, instead, are much weaker than the calculated ones: we interpret this as due to the fact that in solution one does not have only just one ‘‘enantiomeric’’ form, namely that of Figure 2, but also the op-posite one, in unequal amounts, that is to say the enantio-meric excess (ee) between the M- and P-form is quite low. Indeed the calculations suggest that a larger amount of the P-conformer (shown in Fig. 2) is promoted by the L-enantio-meric form ((R,R) in absolute terms) of the diethyl tartrate molecules, while in the other three cases of Figure 1 the P-form of ROT-300 is preferred by the R-enantiomeric P-forms of
Fig. 2. Two different views of an optimized minimum energy geometry of ROT-300 in vacuo obtained by DFT calculation as described in the text. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
TABLE 1. Values of selected dihedral angles of the ROT-300 molecule, as calculated from DFT calculations (for the atomic
numbering see Scheme 1)
Groups Dihedral angles definition Dihedral angles values Perylene unit 16-17-28-31 318 20-19-30-37 318 15-21-36-32 328 N-phenyl–isopropyl groups 1-5-45-43 328 Isopropyl groups 24-22-4-5; 648 27-25-2-1; 648 48-47-46-45; 49-47-46-41 648 51-50-42-43; 52-50-42-41 648
the solvents. We calculate the enantiomeric excess ee as fol-lows16: we define eeð P½ M½ Þ
ð½P þ ½MÞof the P over the M enan-tiomeric form, where [P] and [M] are the concentrations of the ROT-300 compound in a chiral solvent having a given enantiomeric form. In Figure 3 we can measure DA and A, which are defined as:
DA ¼ ðDAPþ DAMÞ ¼ De:l:ð½P ½MÞ ð1Þ
l is the cell path-length;DAMand DAPare the differences
in absorbance of left and right circularly polarized light for the M- and P-enantiomers of ROT-300, respectively; both are related to the molecular quantityDe 5 eLeft2 eRight, the latter
being the difference in absorption coefficients for Left and Right circularly polarized light for pure P species.DA is only due to the imbalance of enantiomeric species in solution. Similarly
A¼ e:l:ð½P þ ½MÞ ð2Þ
wheree 5 (eLeft1 eRight)/2. Using Eqs. 1 and 2 together, we
obtain: DA A ¼ De e ð P½ M½ Þ ð½P þ ½MÞ¼ De e ee ð3Þ In another context, this had been previously defined in Ref. 17. We obtainDA/A for the most intense UV and CD ex-perimental band area of Figure 1 (at 580 nm). We may obtain De/e for the same band in the corresponding calcu-lated spectra of Figure 3: in this way we haveDe/e 5 2.4 3 1024. The results for the ee of either the P over the M form or viceversa due to the use of Eq. 3 to the eight cases of Fig-ure 2 are reported in Table 2.
Abstracting from evident random errors in the measured values, we may state that the ee of one ROT-300 enantiomer over the other one are about 10% for all chiral solvents, except possibly for diethyl-tartrate, where ee is well above this figures. To gain further information on these systems, we took ECD and UV spectra of ROT-300 in diethyl-L-tartrate
and diethyl-D-tartrate at variable temperature, in the range
253 K< T <293 K. The results are given in Figure 4, where we superimpose the ECD spectra from both enantiomeric solvents in the top panel and the UV spectra in the bottom panel (we reiterate that the UV and ECD data were taken at the same time). One may observe that the intensities of the ECD bands increase for all features with decreasing tempera-ture, while the UV spectra do not significantly change. This means that the P-ROT-300/diethyl-L-tartrate preference over
the M-ROT-300/diethyl-L-tartrate increases lowering the
tem-perature. In other words the diastereomeric P-L couple pre-vails over the M-L one to a larger extent when temperature decreases (for the opposite enantiomeric solvent, we observe an increase of the M-D system over the P-D one). In the absorption spectra, there were no significant observable var-iations in frequency or intensity, to make us conclude that the aggregation phenomena reported in the literature18–20
are negligible.
The data of Figure 4 and Table 2 permit the evaluation of thermodynamic quantities involved in the process of chiral recognition. We can define an equilibrium constant K for the reaction M?P in either DLT or DDT, as K ¼ ½P
½M¼ 1þ ee 1 ee(of course K> 1 in DLT and K < 1 for DDT). From the relation DG8 5 -RT ln K, and from the data of Table 2 we have, DG8 5 20.26 Kcal/mol for the DLT solvent at T 5 293 K and DG8 5 10.21 Kcal/mol for the DDT solvent at the same tem-perature.
Fig. 3. Bottom: Experimental (black trace) and calculated (red trace) UV absorption spectrum of ROT-300. Top: Experimental (black and gray traces for DDT and DLT, respectively) and calculated (red trace) ECD spectrum of ROT-300. The bandwidth of 0.14 eV is attributed to the transitions the inten-sity of which is reported as bars. [Here the experimentalDe has been deter-mined from total concentration, namely assuming 100% ee]. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
TABLE 2. |DA/A| ratio and enantiomeric excess of the two enantiomeric species of ROT-300 within the chiral solvents investigated as calculated from Eq. 3 of the text (De/e 5 2.4 3 1024,T 5 293 K)
A |DA| |DA/A| e.e. (%)
(2)-diethyl D-tartrate 30.37 (477–632 nm) 1.383 1023(468–603 nm) 4.523 1025 19 (1)-diethyl L-tartrate 38.7 1.423 1023 3.643 1025 15.2 (S)-(2)-methyl-lactate 81.95 (478–642 nm) 2.243 1023 2.803 1025 11.6 (R)-(1)-methyl-lactate 108.61 1.153 1023 10.563 1026 8.8 (R)-(2)-carvone 65.89 (476–628 nm) 7.533 1024 11.43 1026 4.8 (S)-(1)-carvone 103.51 1.983 1023 19.23 1026 8.0 (R)-(1)-phenylethanol 76.14 (482–642 nm) 1.643 1023(453–610 nm) 2.163 105 9.0 (S)-(2)-phenylethanol 55.19 1.213 1023 2.203 1025 9.2
Here the quoted ee is for either the P over the M form or for the M over the P one (see text).
In Figure 5, we plot the ln K values vs. 1/T with ee data derived from the ECD intensity at various T of the 300 nm band in Figure 4 by the same method as employed in Table 2.
From the vant’Hoff relation in the form: d ln K dð1
TÞ
¼ DH R one has an average value for the DLT (DDT) solution:DH8 5 21.28 Kcal/mol (11.36 Kcal/mol), and from the funda-mental relation DG8 5 DH8 2 TDS8, one has the entropic term DS8, which at room temperature is 23.5 cal/mol.K (13.9 cal/mol K).
An alternative approach for derivingDG8 from ECD data is presented in Refs. 4 and 5, based on previous work.21,22 How-ever in that case no entropic term was present, while here large variations of entropy DS8 are associated either with multiple conformers about the two enantiomers M and P or with different solvation mechanisms possessing the same energy. The general conclusion of the present work is that chiral solvents impair the 50%–50% balanced concentration of the two enantiomeric conformers for ROT-300. In vacuo the latter conformers have equal energy and free energy; in chi-ral solvents one enantiomeric form of the solvent favors one
enantiomeric conformer of ROT-300, the other enantiomeric form favors the opposite one. By running variable tempera-ture ECD spectra on one of the systems, we have provided an experimental measure ofDG8, DH8, and DS8. The precise mechanism and forces involved in the solvent/solute interac-tion and providing the imbalance is unknown, but we point out in Figure 2 that there is a significant red shift of the 585 nm band for phenyl ethanol solvent, possibly meaning that a p-p interaction between solvent and solute is important. How-ever we cannot exclude intermolecular hydrogen bonding interactions which are present for three couples of solvent: only for carvone the latter factors are absent.
CONCLUSIONS
In this work, we have demonstrated that ROT-300 mole-cule, which is an achiral dye, exhibits an equilibrium between enantiomeric conformers. When this dye is dissolved in chiral solvents, an enantiomeric excess appears and is correlated to the chirality of the solvent. We think that the present investi-gations migth be relevant also in emission, due to the peculiar luminescence properties spectra of ROT-300. Finally we asked ourselves whether the same phenomenon be observ-able on other dye-molecules: for this reason we tested the same chiral solvents on Orange-240, i.e., N,N0 -bis(2,6-diiso-propylphenyl)-perylene-3,4:9,10-tetracarboxydiimide but we did not find the same nice intense ECD spectra reported in Figure 2 for ROT-300. In that case, the observed UV features are narrower and the ECD ones are not observed at the experimental conditions adopted for ROT-300. Orange-240 differs from ROT-300 in the substitution of the four O-Phenyl-groups with hydrogen atoms. By DFT calculations, a completely flat central perylene unit is predicted, which makes us think that the O-Phenyl groups of ROT-300 have an important role.
ACKNOWLEDGMENTS
The authors thank the University of Brescia for supporting Marco Passarello. The Researchers from Brescia also thank CILEA for access to their computational facilities and use of Gaussian09.
LITERATURE CITED
1. Stephens PJ, Devlin FJ, Cheeseman JR, Frisch MJ, Rosini C. Determina-tion of absolute configuraDetermina-tion using optical rotaDetermina-tion calculated using den-sity functional theory. Org Lett 2002;4:4595–4598.
Fig. 4. Top pannel: Experimental ECD spectra of ROT-300 in (2)-diethyl D-tartrate and in (1)-diethylL-tartrate at T5 293 K (red and pink curves), T 5 283 K (dark and light purple curves), T 5 273 K (dark and light gray curves), T5 263 K (dark and light blue curves), and T 5 253 K (dark and ligth green curves). Bottom pannel: Experimental absorption spectra of ROT-300 in (2)-diethylD-tartrate at T5 293 K (red curve), T 5 283K (dark purple curve), T5 273 K (dark gray curve), T 5 263 K (dark blue curve), and T 5 253 K (dark green curve). [Experimental absorption spectra of ROT-300 in (2)-diethylL-tartrate are identical]. Solvent spectra subtracted. Spectra taken in 1 mm thermostated cell (10 scans, concentration 43 1024M). [Color fig-ure can be viewed in the online issue, which is available at wileyonlinelibrary. com.]
Fig. 5. Natural logarithm of K equilibrium constant vs. 1/T. The experi-mental values of K are derived from the CD intensity of the 300 nm band of Figure 4 and the method employed in Table 2. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
2. Polavarapu PL. Optical rotation: recent advances in determining the abso-lute configuration. Chirality 2002;14:768–781.
3. Crawford TD. Ab initio calculation of molecular chiroptical properties. Theor Chem Acc 2006;115:227–245.
4. Lightner DA, Gurst JE. Organic conformational analysis. Stereochemistry from circular dichroism spectroscopy. New York: Wiley-VCH; Chapter 4; 2000a. p 63–94.
5. Lightner DA, Gurst JE. Organic conformational analysis. Stereochemistry from circular dichroism spectroscopy. New York: Wiley-VCH; Chapter 5; 2000b. p 95–137.
6. Coulombeau C, Rassat A. Effets de solvant sur le dichroı¨sme circulaire des ce´tones rigides de´rive´es du norcamphre. Bull Soc Chim France 1966;12:3752–3762.
7. Rodger A, Rodger M. Circular dichroism of the carbonyl n-p* transition: an independent systems/perturbation approach. J Am Chem Soc 1988;110:2361–2368.
8. Polavarapu PL. Predictions of chiroptical vibrational properties. Int J Quantum Chem 2006;106:1809–1814.
9. Debie E, Jaspers L, Bultinck P, Herrebout W, Van Der Veken B. Induced solvent chirality: a VCD study of camphor in CDCl3. Chem Phys Lett 2008;450:426–430.
10. Filder J, Rodger M, Rodger A. Chiral solvent structure around chiral mol-ecules: experimental and theoretical study. J Am Chem Soc 1994;116:7266–7273.
11. Stagira S, Nisoli M, Cerullo G, Zavelani-Rossi M, De Silvestri S, Lanzani G, Graupner W, Leising G. The role of amplified spontaneous emission in the ultrafast relaxation dynamics of polymer films. Chem Phys Lett 1998;289:205–210.
12. Osswald P, Wu¨rthner F. Effects of bay substituents on the racemization barriers of perylene bisimides: resolution of atropo-enantiomers. J Am Chem Soc 2007;129:14319–15326.
13. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheese-man JR, ScalCheese-mani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnen-berg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr,
Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Star-overov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O¨ , Foresman JB, Ortiz JV, Cioslowski J, Fox DJ. Gaussian, Inc.: Wallingford, CT, 2009.
14. Furche F, Ahlrichs R, Wachsmann C, Weber E, Sobanski A, Vo¨gtle F and Grimme S. Circular dichroism of helicenes investigated by time-de-pendent density functional theory. J Am Chem Soc 2000;122:1717–1724. 15. Cahn RS, Ingold CK, Prelog V. Specification of molecular chirality.
Angew Chem Int Ed Eng 1966;5:385–415.
16. Brittain HG. Applications of chiroptical spectroscopy in the characteriza-tion of compounds having pharmaceutical importance. In: Berova N, Nakanishi K, Woody RA, editors. Circular dichroism-principles and appli-cations. New York: Wiley-VCH; Chapter 29; 2000. p 819–844.
17. Salvadori P, Di Bari L, Pescitelli G. HPLC-CD: stereochemical analysis at work. In: Berova N, Nakanishi K, Woody RA. Circular dichroism-principles and applications. New York: Wiley-VCH; Chapter 28; 2000. p 797–818.
18. Al-Kaysi RO, Ahn TS, Mu¨ller AM, Bardeen CJ. The photophysical proper-ties of chromophores at high (100 mM and above) concentrations in poly-mers and as neat solids. Phys Chem Chem Phys 2006;8:3453–3459. 19. Wu¨rthner F, Chen Z, Dehm V, Stepanenko V. One-dimensional
lumines-cent nanoaggregates of perylene bisimides. Chem Commun 2006;11: 1188–1190.
20. Kaiser TE, Stepanenko V, Wu¨rthner F. Fluorescent J-Aggregates of core-substituted perylene bisimides: studies on structure-property relation-ship, nucleation-elongation mechanism, and sergeants-and-soldiers prin-ciple. J Am Chem Soc 2009;131:6719–6732.
21. Moscowitz A, Wellman K, Djerassi C. Populations and thermodynamic data from temperature dependent circular dichroism measurements. J Am Chem Soc 1963;85:3515–3516.
22. Moscowitz A, Wellman K, Djerassi C. Effect of solvation upon optically active molecules. Proc Natl Acad Sci USA 1963;50:799–804.
